Question

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Explanation:

Identify the selected option and its mathematical meaning

Using the Absolute Change and Relative Change knowledge points

The selected option is a: "The absolute change is -225 students and the relative change indicates a decrease of 32%."

Let \(V_{\text{initial}}\) be the initial value and \(V_{\text{final}}\) be the final value.

$$ \text{Absolute Change} = V_{\text{final}} - V_{\text{initial}} = -225 $$

This negative value represents a decrease of 225 students.

Verify the relative change calculation

Using the Relative Change knowledge point

$$ \text{Relative Change} = \frac{\text{Absolute Change}}{V_{\text{initial}}} = \frac{-225}{V_{\text{initial}}} = -0.32 $$

$$ V_{\text{initial}} = \frac{-225}{-0.32} = 703.125 $$

A relative change of \(-0.32\) corresponds to a decrease of \(32\%\).
Thus, option a is mathematically consistent and represents the correct interpretation of a decrease in student enrollment.

Answer:

• (a) The absolute change is -225 students and the relative change indicates a decrease of 32%. (Correct answer)
• (b) The absolute change is 225 students and the relative change indicates a decrease of 32%.
• (c) The absolute change is -225 students and the relative change indicates a decrease of 0.32%.
• (d) The absolute change is 225 students and the relative change indicates a decrease of 0.32%.